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Question

If a212ab+4b2=0, prove that log(a+2b)=12(loga+logb)+2log2

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Solution

We have
a212ab+4b2=0

(a+2b)216ab=0,(a+2b)2=16ab...(1)

Takinglogonbothsidesineq....(1)

2log(a+2b)=log(16ab)

log(a+2b)=12log(16ab)

log(a+2b)=12(loga+logb)+12(log16)

log(a+2b)=12(loga+logb)+log1612

log(a+2b)=12(loga+logb)+log4

log(a+2b)=12(loga+logb)+2log2


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